Collocation methods for differential equations with piecewise linear delays

Hui Liang*, Hermann BRUNNER

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

After analyzing the regularity of solutions to delay differential equations (DDEs) with piecewise continuous (linear) non-vanishing delays, we describe collocation schemes using continuous piecewise polynomials for their numerical solution. We show that for carefully designed meshes these collocation solutions exhibit optimal orders of global and local superconvergence analogous to the ones for DDEs with constant delays. Numerical experiments illustrate the theoretical superconvergence results.

Original languageEnglish
Pages (from-to)1839-1857
Number of pages19
JournalCommunications on Pure and Applied Analysis
Volume11
Issue number5
DOIs
Publication statusPublished - Sep 2012

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Collocation methods
  • Delay differential equations
  • Optimal order of superconvergence
  • Piecewise non-vanishing delays
  • Regularity of solutions

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